On the Constrained Capacity of Block Differential Modulation and Detection

In this paper, we consider Block Differential Modulation (BDM), to tackle the phase slip problem in digital communication systems. When the received signal phase can drift, the synchronizer can suddenly choose a wrong reference phase, e.g. adding multiples of 2π/M in case of M-ary Phase Shift Keying. Phase slips are detrimental for any coherent system since they cause long error bursts, till an opposite phase slip occurs. BDM is a generalization of Differential Modulation (DM). Neither of them relies on the absolute carrier phase. However, BDM differentially encodes information between small blocks of symbols and exploits couples of adjacent blocks to decode. This allows simple and practical demapping, without sacrificing capacity. We show that for low and moderate phase slip probabilities, BDM approaches the constrained capacity of coherent transmission, in particular at high spectral efficiencies. We provide closed-form results for the constrained capacity in absence of phase slips for Phase Shift Keying and Quadrature Amplitude Modulation, and we evaluate numerically the constrained capacity through an efficient Monte Carlo method, when phase slips occur. Besides, we provide simple upper and lower bounds.